This paper addresses the problem of stability of a system with uncertainty modelled as a random matrix. The mean of the matrix is assumed to be stable while the variations around the mean model the effect of uncertainty in the parameters. Using some recent advances in random matrix theory, we provide sufficient conditions under which stability is assured with probability one as the dimension of the system increases. This is called limit stability. Our results are stated in terms of a stability margin which corresponds to the size of the variance of the uncertain parameters which can be tolerated.